Abstract

We consider a list decoding algorithm recently proposed by Pellikaan-Wu for q-ary Reed-Muller codes RM{sub q}({ell}, m, n) of length n {le} q{sup m} when {ell} {le} q. A simple and easily accessible correctness proof is given which shows that this algorithm achieves a relative error-correction radius of {tau} {le} (1-{radical}{ell}q{sup m-1}/n). This is an improvement over the proof using one-point Algebraic-Geometric decoding method given in. The described algorithm can be adapted to decode product Reed-Solomon codes. We then propose a new low complexity recursive aJgebraic decoding algorithm for product Reed-Solomon codes and Reed-Muller codes. This algorithm achieves a relative error correction radius of {tau} {le} {Pi}{sub i=1}{sup m} (1 - {radical}k{sub i}/q). This algorithm is then proved to outperform the Pellikaan-Wu algorithm in both complexity and error correction radius over a wide range of code rates.

We present a randomized algorithm which takes as input n distinct points ((x{sub i}, y{sub i})){sup n}{sub i=1} from F x F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., y{sub i} = f (x{sub i}) for at least t values of i), provided t = {Omega}({radical}nd). The running time is bounded by a polynomial in n. This immediately provides a maximum likelihoodmore » decoding algorithm for Reed Solomon Codes, which works in a setting with a larger number of errors than any previously known algorithm. To the best of our knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides some maximum likelihood decoding for any efficient (i.e., constant or even polynomial rate) code.« less

As the volume of data acquired by space-based sensors increases, mission data compression/decompression and forward error correction code processing performance must likewise scale. This competency development effort was explored using the General Purpose Graphics Processing Unit (GPGPU) to accomplish high-rate Rice Decompression and high-rate Reed-Solomon (RS) decoding at the satellite mission ground station. Each algorithm was implemented and benchmarked on a single GPGPU. Distributed processing across one to four GPGPUs was also investigated. The results show that the GPGPU has considerable potential for performing satellite communication Data Signal Processing, with three times or better performance improvements and up to tenmore » times reduction in cost over custom hardware, at least in the case of Rice Decompression and Reed-Solomon Decoding.« less

This paper reports on design technique to harden CMOS memory circuits against Single Event Upset (SEU) in the space environment. The design technique provides a recovery mechanism which is independent of the shape of the upsetting event. A RAM cell and Flip Flop design are presented to demonstrate the method. The Flip Flop was used in the control circuitry for a Reed Solomon encoder designed for the Space Station and Explorer platforms.

This paper presents FPGA implementation of the Reed-Solomon decoder for use in IEEE 802.16 WiMAX systems. The decoder is based on RS(255,239) code, and is additionally shortened and punctured according to the WiMAX specifications. Simulink model based on Sysgen library of Xilinx blocks was used for simulation and hardware implementation. At the end, simulation results and hardware implementation performances are presented.

A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selectingmore » repeats iteratively until either all of the columns are populated or the number of currently unpopulated columns exceeds the number of vectors in the reduced set. Columns for the check matrix may be processed to reduce the amount of logic needed to implement the check matrix in circuit logic.« less